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Surface Area ad Volume of A Right Circular Cone - Class 9 : Notes


(1) A right circular cone is a solid generated by revolving a line segment which passes through a fixed point which makes a constant angle with a fixed line. The fixed point is called the vertex of the cone,  the fixed line is called the axis of the cone.

(2)For a right circular cone of base radius r,  slant height l and height h, we have

(i) Curved surface area  = \pi rl
For Example:

If radius r = 5cm, length l = 7cm, then
Curved surface area  = \pi \times 5 \times 7 = 109.9c{m^2}

(ii) Total surface area  = \pi r(l + r)
For Example: If radius r = 5cm, length l = 7cm, then
Total surface area  = \pi \times 5(7 + 5) = 188.4c{m^2}

(iii) Volume  = {1 \over 3}\pi {r^2}h
For Example: If radius r = 5cm and height h = 10cm, then
Volume  = \frac{1}{3}\pi \times {5^2} \times 10 = 261.66c{m^3}

Also, Volume  = {1 \over 3}(Area of the base) \times height
For Example: Volume  = \frac{1}{3}(78.5) \times 10 = 261.66c{m^3}

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